x Turn on thread page Beta
 You are Here: Home >< Maths

Stochastic processes - Exponential r.v's watch

1. Hey guys, while doing some research on stochastic processes I have same round a couple of problems:
1. U=min{X,Y}, V=max{X,Y}, X,Y are independent EXP(lambda) and EXP(mu) r.v's (respectively). What is E(V-U).
2. b N_t is Poison(15) process. What is P(N_8=10|N_9=6); what is P(N_9=6|N_8=10);

For the first problem I have came up with the flowing idea: V-U=|X-Y|. Then P(|X-Y|<x)=P(X-Y<x|X>Y)+P(Y-X<x|Y>X). How can I calculate these probabilities ie P(Y>X)? Than I could calculate the density function and integrate to obtain E(V-U). Or is my approach wrong?
As for the second problem, since Poison process is increasing than these probabilities are equal to 0. Am I right?

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: April 10, 2011
Today on TSR

Did he block me?

What should I do?

Poll
Useful resources

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

How to use LaTex

Writing equations the easy way

Study habits of A* students

Top tips from students who have already aced their exams

Chat with other maths applicants